✒️Expressions
[tex]••••••••••••••••••••••••••••••••••••••••••••••••[/tex]
[tex] \huge{\colorbox{black}{\color{lavender}{\tt{‡ANSWERS‡}}}}[/tex]
→ 1.) [tex]\small\color{green}\boxed{4x³ +5}[/tex]
→ 2.) [tex]\small\color{green}\boxed{4x² - x + 3}[/tex]
→ 3.) [tex]\small\color{green}\boxed{2x² + x - 11}[/tex]
→ 4.) [tex]\small\color{green}\boxed{11x - 13x²}[/tex]
→ 5.) [tex]\small\color{green}\boxed{7x² + 6x - 3}[/tex]
→ 6.) [tex]\small\color{green}\boxed{2x² - 3x + 3}[/tex]
[tex]••••••••••••••••••••••••••••••••••••[/tex]
[tex] \large{\colorbox{black}{\color{gold}{\tt{♪Step\:by\:Step\:Solution♪}}}}[/tex]
1.) Solution number 1. ↓
Step 1↓
Remove unnecessary parentheses
[tex]6{x}^{3} - 4 + (2 {x}^{3} + 9)[/tex]
When there is a + in front of expression in parentheses, the expression remains the same
[tex]6 {x}^{3} - 4 - 2 {x}^{3} + 9[/tex]
Step 2↓
Collect like terms
[tex]4 {x}^{3} - 4 + 9[/tex]
Calculate the sum
[tex]4 {x}^{3} + 5 [/tex]
2.) Solution number 2.↓
Step 1↓
Remove unnecessary parentheses
[tex]x + 5 + ( - 2x + 4 {x}^{2} - 2)[/tex]
When there is a + in front of expression in parentheses, the expression remains the same
[tex]x + 5 - 2x + 4 {x}^{2} - 2[/tex]
Step 2↓
Collect like terms
[tex] - x + 5 + 4 {x}^{2} - 2[/tex]
Subtract the numbers
[tex] - x + 3 + 4 {x}^{2} [/tex]
Step 3↓
Use the commutative property to reorder the terms
[tex]4 {x}^{2} - x + 3[/tex]
3.) Solution number 3.↓
Step 1↓
Remove unnecessary parentheses
[tex] {x}^{2} + x + ( {x}^{2} - 11)[/tex]
When there is a + in front of expression in parentheses, the expression remains the same
[tex] {x}^{2} + x + {x}^{2} - 11[/tex]
Step 2↓
Collect like terms
[tex]2 {x}^{2} + x - 11[/tex]
4.) Solution number 4.
Step 1↓
Remove unnecessary parentheses
[tex]8x - 4 {x}^{2} + (3x - 9 {x}^{2} )[/tex]
When there is a + in front of expression in parentheses, the expression remains the same
[tex]8x - 4 {x}^{2} + 3x - 9 {x}^{2} [/tex]
Step 2↓
Collect like terms
[tex]11x - 4 {x}^{2} - 9 {x}^{2} [/tex]
Collect like terms
[tex]11x - 13 {x}^{2} [/tex]
5.) Solution number 5.
Step 1↓
Remove unnecessary parentheses
[tex]2 {x}^{2} + 6x + 4 + (5 {x}^{2} - 7)[/tex]
When there is a + in front of expression in parentheses, the expression remains the same
[tex]2 {x}^{2} + 6x + 4 + 5 {x}^{2} - 7[/tex]
Step 2↓
Collect like terms
[tex]7 {x}^{2} + 6x + 4 - 7[/tex]
Calculate the difference
[tex]7 {x}^{2} + 6x - 3[/tex]
6.) Solution number 6.
Step 1↓
Remove unnecessary parentheses
[tex]3 {x}^{2} - x + 11 - ( {x}^{2} + 2x + 8)[/tex]
When there is a – in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses
[tex]3 {x}^{2} - x + 11 - {x}^{2} - 2x - 8[/tex]
Step 2↓
Collect like terms
[tex]2 {x}^{2} - x + 11 - 2x - 8[/tex]
Collect like terms
[tex]2 {x}^{2} - 3x + 11 - 8[/tex]
Subtract the numbers
[tex]2 {x}^{2} - 3x + 3[/tex]
[tex]••••••••••••••••••••••••••••••••••••••••••••••••[/tex]
^_^
